During running of a vehicle including a direct injection engine directly injecting fuel into a cylinder, an engine is repeatedly restarted in some cases. For example, this corresponds to a so-called idling reduction vehicle restarting a direct injection engine after the engine is automatically stopped each time the vehicle stops running for the purpose of fuel consumption saving, exhaust emission reduction, and noise reduction and to a hybrid vehicle restarting a direct injection engine in accordance with an increase in request output so as to make a shift from previous electric motor running to engine running. The direct injection engines in such vehicles use a so-called ignition start by injecting and sparking fuel in a cylinder in an expansion stroke out of multiple cylinders and the rotation of the direction injection engine is raised by utilizing a torque generated by explosion due to this sparking.